Rapid heating and cooling can make some materials brittle, but generally you'd need to heat a substance to the point that it's nearly melted in order to risk damage from cooling it back down. So unless your floor gets hot enough to melt plastic, you should be fine (and if it does, you have bigger problems than a few melted minifigs).

Um... heat usually doesn't, but every now and then Lego gets a shipment of plastic pellets with some kind of impurity in them that causes the plastic to develop cracks over time during normal use - the cracks are usually along seam lines, but sometimes right in the middle of a flat surface. Several of the original Pirate sets that I got when I was a kid developed cracks like those. Doesn't happen often, but it does happen. Could also be from the plastic cooling too quickly during casting so it doesn't "meld" properly...

I think this is a question I could answer correctly. As much as I know thermal cracking of ABS could occur right after the manufacture process when hot plastic cooled down but reheating could not lead the parts to crack.